Question

the hypotenuse of the right triangle is 13 units, the adjacent leg is 12 units, the opposite leg is 5 units, find he angle degree using the inverse of cosine for the angle between the hypotenuse and the adjacent leg. round your answer to the nearest tenth

Answer 1

To find the angle between the hypotenuse and the adjacent leg using the inverse cosine function (\(\cos^{-1}\)), we can use the following formula:

\[
\theta = \cos^{-1}\left(\frac{\text{adjacent leg}}{\text{hypotenuse}}\right)
\]

Given:
- Hypotenuse = 13 units
- Adjacent leg = 12 units

We substitute these values into the formula:

\[
\theta = \cos^{-1}\left(\frac{12}{13}\right)
\]

Now calculate the value of \(\frac{12}{13}\):

\[
\frac{12}{13} \approx 0.9231
\]

Now, find the inverse cosine:

\[
\theta = \cos^{-1}(0.9231)
\]

Using a calculator:

\[
\theta \approx 22.6 \text{ degrees}
\]

Rounded to the nearest tenth, the angle between the hypotenuse and the adjacent leg is approximately:

\[
\theta \approx 22.6 \text{ degrees}
\]